Issue 55

V. Yu. Popov et alii, Frattura ed Integrità Strutturale, 55 (2021) 136-144; DOI: 10.3221/IGF-ESIS.55.10

Figure 6: Relaxation and long-term strength curves for 08Cr16N11M3 steel for the initial stress of 200 MPa and the temperature of 600 °C.

R ELIABILITY ASSESSMENT

Method n the general case, the strength reliability is determined through the probability of failure-free operation P , which is gotten by integrating the probability density function   Ψ p of the difference of random variables R - alleged failure stresses, with the mathematical expectation R and F - of the calculated stresses, with the mathematical expectation F :   Ψ p =    p R F (Fig. 7), in the interval determining the failure-free operation, on which the values of R ≥ F , i.e. from 0 to +  .                      2 2 0 Ψ 1 2 2 P exp d (9) where  – the integration variable;   – standard deviation of a random variable  , according to the rule of summation of random variables, the square of which  2 Ψ is equal to the sum of the variances D R =  2 R and D F =  2 F :      2 2 2 Ψ R F [6], from where                 2 2 2 2 R F R F R F (10) where  R and  F are the object of the investigation - are the coefficients of variation of the random variables R and F; Ψ - the mathematical expectation of a random variable, in this case, the meaning of the mathematical expectation difference   Ψ R F . To take into account the change in the reliability characteristics over time, use the relaxation curve as a function describing the change in the calculated stresses   F t , and the long-term strength curve as a function describing the change in the stress of the alleged failure   R t , and obtain         Ψ t R t F t . Then can be built (for example, in MATLAB or Python) a three-dimensional function of probability density over time, taking into account the change in time of all its parameters (Fig. 8) [7, 8] and the function of changing the probability of failure-free operation over time (Fig. 9). I

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